Question

for my homework assignment I’m to generate a set of numbers to a fixed point that allows for the mean to be 0 and the standard deviation to be 1. I’ve been mainly dealing with an array of doubles to attempt this but I’m not sure how to accomplish this.

For generating the values, I’ve tried using Box Muller method but I still end up with a mean and standard deviation thats still off from the mark of mean = 1 and sd = 1 for standard normal distribution

UPDATE: Okay, I just realized my mistake. For box muller, I mistyped the 2 for a 3 instead. Fixed the problem now.

//Create Standard Normal Distribution
void std_find(double a[],double s[], int pop, int samp){//
    //generate random numbers for std normal
    double *p;
    p = a;
    //generate numbers in standard normal
    double numA = 0;
    double numB = 0;
    double PI = 3.14159;
    //Box_Muller
    for(int i = 0; i < pop; i= i+2){
        numA = (rand() * 1)/(double)32767;
        numB = (rand() * 1)/(double)32767;
        *p = sqrt((double)-3 * (log(numB))) * cos((double)3* PI*numA);
        p++;
        *p = sqrt((double)-3 * (log(numB))) * sin((double)3 *PI*numA);
        p++;
    }
    double popMean = mean(a,(double)pop);
    //double popMean = (double)0;
    double popSD = sqrt(sampleV(a,pop));
    //double popSD = (double)1;
    cout << "\nPopulation Mean of the std: " << popMean;
    cout << "\nPopulation Standard deviance of std: " << popSD;
    //population created, now to create sample
    sample(a,s,samp,popMean,popSD);
    }

Answer 1

A good general way to go about this is to generate numbers that follow a standard normal distribution (defined as a normal distribution with µ=0 and σ=1). Take a look at the Wikipedia article for the normal distribution, specifically the section that says “Generating values from normal distribution”.